Hurwitz' theorem on composition algebras
Bruce W. Westbury
TL;DR
This paper explains a diagrammatic proof of Hurwitz's theorem, which classifies composition algebras by their possible dimensions: 0, 1, 2, 4, or 8.
Contribution
It provides an exposition of Boos and Rost's diagrammatic proof of Hurwitz's theorem on composition algebra dimensions.
Findings
Confirmed the possible dimensions of composition algebras
Presented a clear diagrammatic proof approach
Enhanced understanding of algebra classification
Abstract
The main aim of this article is to give an exposition of the diagrammatic proof due to Boos and Rost of the theorem of Hurwitz that the dimension of a composition algebra is one of 0,1,2,4,8.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Advanced Algebra and Logic